Filter and method for its manufacture

ABSTRACT

An electromechanical filter having a first and a second transducer resonator and a plurality of additional resonators, each resonator having first and second end surfaces. The resonators are arranged substantially parallel to one another. Two longitudinally vibrating thin, coupling wires are respectively coupled to the first end surfaces and to the second end surfaces. A plurality of thin, metal mounting strips are fastened to the resonators. The thickness d, and length 1, of each of the mounting elements corresponds approximately to the equation:

United States Patent Borner et a1.

FILTER AND METHOD FOR ITS MANUFACTURE Assignee:

Filed:

Appl. No.: 283,277

Inventors: Manfred Borner; Hans Schussler,

both or Ulm/ Danube, Germany Licentia Patent-Verwaltungs-G.m.b.I-I.,Frankfurt, Germany Aug. 24, 1972 [30] Foreign Application Priority DataAug. 24, 1971 Gennany 2142332 [52] US. Cl 333/72, 29/2535, 310/8.2,333/71 [5 I] Int. Cl "03h 9/04, H03h 9/26 [58] Field of Search 29/2535,169.5; 333/72, 333/71, 30; 3l0/8.2-8.5, 9.1, 26

[56] References Cited UNITED STATES PATENTS 2,647,949 8/1953 Burns, Jr310/26 X 2,845,697 8/1958 Adler 29/1695 2,870,521 1/1959 Rudnick 29/25353,086,182 4/1963 Borner i. 333/30 R X [451 Apr. 30, 1914 3,717,8282/1973 Arleevskaya et a1. 333/71 FOREIGN PATENTS OR APPLICATIONS1,541,975 12/1969 Gemiany 333/71 Primary Examiner-James W. LawrenceAssistant Examiner-Marvin Nussbaum ABSTRACT An electromechanical filterhaving a first and a second transducer resonator and a plurality ofadditional resonators, each resonator having first and second endsurfaces. The resonators are arranged substantially parallel to oneanother. Two longitudinally vibrating thin, coupling wires arerespectively coupled to the first end surfaces and to the second endsurfaces. A plurality of thin, metal mounting strips are fastened to theresonators. The thickness d, and length l, of each of the mountingelements corresponds approximately to the equation:

Such an electromechanical filter is manufactured by fixing each of theresonators to mounting elements, and removing material as required fromat least one of the resonators to effect tuning.

21 Claims, 12 Drawing Figures PAIENTEB 30 SHEU 2 BF 2 FILTER AND METHODFOR ITS MANUFACTURE BACKGROUND OF THE INVENTION This invention relatesto an electromechanical filter and to a method of making the filter. Thepresent invention relates, more particularly, to an electromechanicalfilter having resonators of the flexural vibration type andlongitudinally oscillating coupling elements as well aspiezoelectrically acting transducer resonators at its input and itsoutput.

Mechanical filters with a frequency of about 50 kHz and a bandwidth ofabout 3 kHz have recently gained particular importance primarily becausea carrier frequency system is about to be introduced which uses channelfilters having this frequency capability. Thus an eminently importantsituation has developed for electromechanical filters. 1

While thus far performance qualities were of foremost importance andprincipal research in the electromechanical field has been directedthereto, the emphasis in the field of these filters has now shifted toproduction techniques and substantial automatization.

SUMMARY OF THE INVENTION It is an object of the present invention toprovide an electromechanical filter which can be very economicallyfabricated.

It is another object of the present invention to provide a simpleeconomical method of fabricating electromechanical filters.

One purpose is to eliminate production steps, if necessary at thesacrifice of higher quality, if this were to exceed, to too large anextent, the minimum requirement for the filter tolerances.

It has been found, in practicing the present invention, that there are aseries of previously unknown practices and constructions which permitsimplification of the fabrication process and even an improvement inquality to some extent. Thus it is possible to lower quality demands atother points in the fabrication process. The present invention thereforeresides in a combination of features which optimizes the total filterdesign in the desired manner.

The invention, in its apparatus aspect, resides in an electromechanicalfilter having an input arrangement formed by a first piezoelectricallyacting transducer resonator, having first and second end surfaces. Anoutput arrangement is fonned by a second piezoelectrically actingtransducer resonator, having first and second end surfaces. A pluralityof intervening resonators of the flexural vibrating type, each havingfirst and second end surfaces, are provided. The transducer resonatorsand the intervening resonators are arranged substantially parallel toone another. Two longitudinally vibrating coupling elements in the formof thin coupling wires, are provided. One of the coupling elements iscoupled to each of the first end surfaces and the other coupling elementis connected to each of the second end surfaces. A plurality of mountingelements in the form of respective, thin, metal strips are fastened tothe resonators of the plurality of resonators and to the transducerresonators. The thickness and the length of the mounting elementscorrespond approximately to the equation:

where d is the thickness of the metal strips, I is the length of themetal strips, m is the angular (radial) frequency of the filter, p isthe dei'tsity of the metal strips, E is the modulus of elasticity of themetal strips and a is a constant.

The end surfaces to which two of the coupling wires are fastened arepreferably the frontal faces of the intervening resonators andtransducer resonators so that the succession of end surfaces throughoutthe filter are connected together by at least one continuous wire.

The constant or preferably has a value of 0.62, for M4 type behavior; 0.I I5 for 3)\ l 4 type behavior; and 0.046 for 5M4 type behabior.

The invention in its method aspect, involves the making of anelectromechanical filter which includes providing a first transducerresonator, a second transducer resonator, and a plurality of interveningresonators, fixing each of the intervening resonators and each of thetransducer resonators to mounting elements, and removing material asrequired from at least one of the resonators to effect tuning thereof.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. I is a perspective view of oneembodiment of an electromechanical filter constructed in accordance withthe present invention, some of the resonators being absent, for the sakeof clarity, and one resonator being shown in section.

FIG. 2 is a perspective view of a plurality of resonators coupledtogether by a wire.

FIG. 2A is a diagrammatic illustration of a resonator and an associatedcoupling wire of the single coupling wire type, with the coupling wiredisplaced from the center of the resonator.

FIG. 3 is a graphical representation of the coupling ratio (K/K plottedagainst the ratio of the distance that the coupling wire, as showngenerally in FIG. 2A, is from an end of the resonator to the half lengthof the resonator (I /h).

FIG. 4 is a graphical representation of the frequency characteristics ofan electromechanical filter constructed in accordance with the presentinvention.

FIG. 5 is a diagrammatic, perspective view of a mounting elementsuitable for use as part of an electromechanical filter constructed inaccordance with the present invention.

FIG. 6 is a perspective view of a second embodiment of a mountingelement suitable for use as part of an electromechanical filterconstructed in accordance with the present invention.

FIG. 7 is a perspective view of a mounting arrangement composed of aplurality of mounting elements formed by a common metal piece.

FIG. 8 is a perspective view of a transducer resonator suitable for useas part of an electromechanical filter constructed in accordance withthe present invention.

FIG. 9 is a plan view ofa plurality of intervening reso nators and atransducer resonator coupled together by wires in accordance with apreferred embodiment of the present invention.

FIG. 10 is a plan view ofa plurality of resonators and a transducerresonator coupled together by wires in accordance with a furtherpreferred embodiment of the present invention.

FIG. 11 is a perspective view of one embodiment of an electromechanicalfilter constructed in accordance with the present invention comprisingadditional cou pling wires between nonadjacent resonators.

DESCRIPTION OF THE PREFERRED EMBODIMENTS FIG. 1 illustrates anembodiment of an electromechanical filter constructed in accordance withthe pres ent invention. The economic and technological advantage of thepresent invention is to be explained with the aid of FIG. I. As shown inFIG. 1, the electromechanical filter according to the present inventionincludes electromechanical transducers and a mechanical filter structurewhich transmits purely mechanical waves, in its transmission range, andreflects them, in its blocking range. In order to achieve this, a seriesof intervening resonators 2 which generally are made of a special metalalloy are disposed between an input piezoelectrically acting transducerresonator l and an output trans ducer resonator I. For the sake ofclarity, only three of the resonators 2 are shown in FIG. 1, one insection, so as to show more clearly other parts of the electromechanicalfilter. However, in the illustration, eight intervening resonators areto be provided.

The housing includes a cover 6 which is shown broken away to exposeelements [-4, connected, by conventional means, to a mounting plate 5 onwhich the mounting elements 4 are fixed. The mounting elements 4 are, asshown in FIG. 1, thin metal strips fonned from parts of a thin metalmember which is fixed, for example by welding, to the mounting plate 5.A piezoelectric member 8, preferably in the form of a ceramic mem' her,is fixedly positioned on a surface of the second transducer resonator I.A lead 7', on which the output signal from the filter appears, isconnected to an electrode of the piezoelectric member 8. Another similarpiezoelectric member (not visible in FIG. 1) is fixedly attached to asurface of the first transducer resonator l, a lead 7 being provided toan electrode of this transducer to serve as the signal input lead of thefilter. 66

All of the resonators I, l' and 2, as shown in FIG. I, are connected insuccession by means of coupling elements 3, e.g. thin wires preferablyconnected to the resonator end faces. Nonadjacent ones of the resonatorsmay be additionally coupled together in any of many possible ways. Inthe first case, the electrical equivalent circuit diagram exhibits thecharacteristics ofa polynomial filter. With the additional coupling, itis possible to produce attenuation peaks at real and complexfrequencies. It is also of importance that the coupling elements 3 havea given length which is related to the wavelength of the oscillationsought to be passed through the electromechanical filter.

A very decisive role is played by a plurality of substantiallyidentically dimensioned, mechanical mounting elements 4 for theresonators l, l' and 2. Two of the mounting elements 4 are provided foreach of the resonators l, l and 2, and are fixed to spaced points of therespective resonators l, l and 2 inwardly of their end surfaces, towhich the coupling elements 3 are fixed.

The mounting elements 4 serve to decouple the filter as completely aspossible from the housing 5, 6. The mounting elements 4 must be stable,can be produced inexpensively, and must not detune the resonators l, 1'and 2 or only detune them in a consistently repeatable manner, i.e. bythe same amount from one production unit to the next. The resonators l,I and 2 must not have additional resonant points (ancillary waves) as aresult of their association with the mounting elements 4; any existingundesired resonances must be either attenuated or displacedintorioninterfering frequency regions.

The cover 6 is of importance because of the ancillary waves, if flexuralresonators are used whose sound irradiation cannot be neglected,particularly in the range of about 50 kHz. Generally proven structurescan be dependably used.

This leads to the subject of the problems which must be particularlyconsidered in connection with a filter operating at a frequency of about50 kHz. Since the dimensions of known longitudinal and torsionresonators would become much too large, lengths of about 50 mm or about28 mm being required, only flexural resonators can realistically beconsidered. In this regard, there exists a prior proposal, as showngenerally in FIG. 2, to couple the resonators l0 of an electromechanicalfilter by means ofa single wire 11 which vibrates longitudinally. Thisknown technique is disclosed in German Patent No. l,l00, 834 and inGerman Laid Open Patent Applications Nos. l,922,55l and l,54l,975. Atthis point, dual criteria may be applied, which lead to a first partialunderstanding of the theory of the invention described herein. Since theA/4 length of the longitudinal vibration in the coupling wire is, at afrequency of 50 kHz, 25 mm, the coupling length, in order to reduce theoverall structural length, must be 25mm, i.e. practically a length of5mm.

If the influence of the temperature coefficient of the longitudinalspeed of sound on the position of the filter edges is calculated forsuch a filter, it can be found that the only coupling wire suitable forthis purpose is fonned from a special nickel-iron alloy, such as is soldunder a number of trade names, e.g. Ni-Span-C, Thermelast or the like,after it has been subjected to a special heat treatment. Ni-Span-C is aNi-Fe alloy consisting of 42,5 Ni, 5 Cr, l Al and Ti, remainder Fe. Thecomponents of Therrnelast are as follows: 42 Ni, 9 Mo, l Be, remainderFe.

If M4 coupling were used, it would have been possible to do without thespecial alloys mentioned above. In practice this means, over and beyondthe heat treatment which can be easily mastered, that wires with verysmall diameter tolerances, about :1 micron, must be made from a charge.This is not possible, however, with sufficient uniformity throughout thefabrication process using the alloys mentioned above compared with wiresof a well-known nickel-iron-molybdenum alloy, which in the tube art arecalled A-wires and which have served extraordinarily well for M4coupling. A-wire material consists of Ni, Fe and Mo. It is, therefore, apreferred feature of the present invention to employ two coupling wireswhich are so combined, from the different existing drawing charges, thatthe sum of the cross sections of the two wires corresponds to the totalcoupling wire cross section required for the value of the total couplingwhich is to be accurately maintained.

When only one coupling wire II is used for coupling, it initiallyappears to be of advantage to attach this wire 11 at the center of thefiexural resonators 10, as shown in FIG. 2. However, if the efficiencyof such a coupling is considered, it will be found that in order toobtain a certain band width in the center of the resonators l0,

the coupling wire 11 must have a cross section which is greater by thefactor l/0.37 2.7 (FIG. 3) as can be learned from an article in thepublication AEU I6 (1962) (Archiv der Elektrischen Ubertragung), S. Hirzel Verlag, Stuttgart, West Germany, pages 355-358. Experience has shownthat in a channel filter operating at a frequency of about 50 kHz andwith the use of a single wire ll in the center of the resonators l l, Iin FIG. 2a), the diameter of the coupling wire 11 is about 0.45mm. Iftwo wires serving as the coupling members 3 (FIG. 1) are used insteadand connected at the two end surfaces of the resonators l, 1' and 2, inaccordance with the present invention, the diameter of these couplingwires reduces to 0.45 l/ V? l/ 2.7mm 0.]9mm. This reduction in the crosssection is very decisive in another respect. As can be seen in FIG. 3,the coupling ratio decreases as the single coupling wire 11 is movedaway from the center point, reaching zero at a l ratio of about 0.3 andthereafter reaching l.0 when l, is zero; i.e., the wire 11 is at the endof the resonator 10.

FIG. 4 shows graphically how strongly the frequencies shift at the upper(f,) and lower (L) edges of the band as well as at the center bandfrequency f when the length of a coupling member I differs from M4. Thefrequencies are standardized to the prealignment frequency f, of theresonators inherent to them before the coupling members or wires arewelded on. K is the coupling factor of the resonators. The steep rise ofthe curves directly shows that for f, and f at I, )t/4 the maintainingof an accurate coupling length is very critical. For a SOkI-Iz channelfilter with I mm A/2O) the permissible tolerances for the filter resultin a manufacturing accuracy of the length I of Al, 2 i4p.

The position of the welding point for welding the coupling wire to theflexural resonator must be corre spondingly accurate. The advantage ofusing two coupling wires, in accordance with this invention, each havinga diameter of 190p. instead of one wire with a diameter of 450p. becomesimmediately evident. In principle, a wire of 190p. can be welded muchmore accurately than a wire of 45044.. Added to this advantage is afurther advantage when the proposed two coupling wires are welded to thetwo frontal faces of the resonators, in accordance with the presentinvention. The position of a coupling wire and its thickness aredecisive, with regard to the degree (strength) of the coupling effectedby the coupling wire, but not its accurate positioning on the frontalface of the resonators. When only one coupling wire is used, which isattached to the center of the resonators, the accurate positioning ofthis point is also decisive as can be seen from FIG. 3 (with I, z l,).The value K K is thus dependably achieved in the arrangement of thepresent invention over the entire frontal face. This is of importancefor the manufacture of the filters.

An electromechanical filter according to FIG. I is to be manufactured insuch a way that first all parts of the filter shown in FIG. I, exceptfor the coupling elements (wires) 3, are connected together, forexample, by electrical spot welding, soldering or cementing. Then theindividual resonators 2 and the transducer resonators l and 1' areaccurately frequency tuned. The weld ing jig in which the resonators 2and the transducer resonators I and l are welded to the mountingelements 4 need not meet any extreme precision requiremenLs. A spacingtolerance of about :0. lmm in the alignment of these parts ,to oneanother is sufficient for the type of filters according to the presentinvention. The very decisive process of welding on the coupling elements(wires) 3 of the prescribed length l, i 4;; can then be effected withthe utmost precision, for example with special precautions in anaccurate, adjustable jig. It is then, however, not necessary to observesimultaneously the accurate positioning of the welding point on theresonators 2 and on the transducer resonators I and 1'.

Since the importance of the arrangement of the resonators 1,1 and 2 andthe coupling elements (wires) 3 in FIG. I has now been made clear. afurther point which brings practical success to this arrangement is themounting of the resonators 2 and transducer resonators l and l'.

The difficulty here again is the attainment of relatively short mountingelements 4. In principle, ultrasonic vibrations will always propagatealong the mounting elements 4. Depending on whether the propagatingenergy is reflected or absorbed,- the mounted resonators I, I and 2 aredetuned or attenuated. The magnitude of these effects can be reduced byproviding a cross section for the mounting element 4 which just sufficesfor mounting purposes, so that the coupling of the mounted resonators 1,l' and 2 with the cover 6 and the mounting plate 5 is reduced in thatthe acoustically effective length of these mounting elements 4 is madeabout M4. This is possible in an arrangement such as shown, for example,at 4 in FIGS. 1 and 2 of the German Laid Open Patent Application No.l,022,550, only when the length of the holding pins is about l4mm. Thetorsional vibrations transmitted from the holding pins would beoptimally decoupled from the housing.

In the design of the filter according to FIG. 1 hereof a novel approachis taken which will be explained with the aid of that figure. Themounting elements 4 in FIG. 1 each substantially consist of an actualsupporting part which is shown, in an enlarged view, in FIG. 5 and whichhas a length L, a width b and a thickness d. This element is torsionallystressed by that one of the resonators l, l' and 2 with which it isassociated, and performs flexural vibrations in the plane of theresonators l, l' and 2. If this mounting element is imagined to beseparated into parallel sections along the dashed lines shown in FIG. 5,the individual sections perform flexural vibrations. Nothing changes inthe mechanism of these vibrations in a first approximation, i.e. at alow amplitude, if the separation is not made. The thickness value d canbe detemiined, for example, with the aid of an experiment set forth inthe periodical AEU l5 (l96l), Issue No. 4, pages -180, equations (la)and (20a) of which are of interest. when the length of the mountingelement is given and there is a )t/4 type coupling. The followingapplies:

where E/p 5 l0cm/sec, the speed of sound for longitudinal waves. E isthe modulus of elasticity. The symbol p is the density of the material.The symbol to is the angular frequency; i.e., w, 21rf,,, f being thecenter frequency of the filter. and

where J is the geometrical moment of inertia of the cross-sectionalmounting element shown in FIG. with the width Ab and the thickness dabout an axis in the direction of the edge having the length Ab. lt canbe seen that the value b, or Ab, is derived from the calculations of theM4 length for mounting elements and this again justifies the assumptionthat a mounting element according to FIG. 5 can be separated, foranalytical purposes, into segments in the manner shown by the dashedlines.

The above equations thus result in:

d/l (0,, VplE 0.62

for M4 type coupling, the units for d and 1 being in cm.

lfl 0.3cm is selected, the following applies at a frequency: f, to /21750 kHz d 0.035cm 4 in an entirely analogous manner, the correspondingformulas result for the relationships, for example, at 3M4 and 5M4 typecoupling, i.e.

for 3M4 type coupling and d/l w, v TE 0.046

for 5M4 type coupling.

An advantageous further embodiment of a mounting element suitable foruse in the present invention is shown in H0. 6. The mounting elementconsists, at least in its portion which is torsionally stressed, of aframe having approximately the following inner dimensions:

L' L and b %L' to A: L'.

With such a configuration of the mounting element it is possible toobtain even better decoupling between the resonators 2 or transducerresonators l and l, and the housing cover 6 and the support plate 5.

The width b is adapted to that of the resonators 2 or that of thetransducer resonators l and I. In practice, b will be approximately 2mm.Thus the entire arrangement has suitable stability in addition tooptimum decoupling.

Advantageously the M4 long mounting elements 4 (FIG. 1). as morespecifically shown in FIGS. 5 or 6, are to be provided usingconventional principles employed for the construction of filters and thearrangement of the resonators l, l' and 2 thereon. The mounting elements4, as shown in FIG. 1, are of a common metal piece, are to be made, forexample, by stamping, and are to be bent in such a manner that anintegral body results. as shown in FIG. 7. This produces good stabilityduring the first fabrication steps, and results in a stable. sturdymounting arrangement.

This stability is particularly important since, after assembly of theparts of the filter shown in FIG. 1, or before welding on the couplingwires 3, the resonators 2 and the transducer resonators 1 32d I must beturned. Either because of their precise fabrication or as a result of afirst prealignment before being welded to the mounting elements 4 theyalready have an approximately correct resonant frequency and band width.However, the. first welding step produces such stray phenomena thatsubsequent tuning, in the range of a few Hertz, is generally needed atthis point. The magnetic fields produced as a result of electricwelding, if such a technique is used, have an influence on the in herentfrequency which must be eliminated by a demagnetization process.

The actual tuning process can be effected by grinding with a finehigh-speed grinding disc or the like. It is best to grind the end ofresonators and thus increase the frequency. This retains thecharacteristic impedance Z of the resonators l, l and 2 and thus alsothe degree of coupling between the adjacent resonators at a given crosssection of the coupling wires 3.

it should be mentioned at this point that the coupling between theresonators must be able to meet the requirements of filter theory,generally the coupling decreases from the outer to the inner resonatorpairs by a factor of 2, or more. With a constant spacing 1 between theresonators and a constant cross section of the coupling wires 3, thiscan be accomplished only by varying the cross section of the resonatorsl, l and 2.

It is much more practical, however, to slightly vary the lengths 1 andthus set the coupling between the resonators l, l and 2. The tuningfrequencies between the individual resonators 2 and between thetransducer resonators l and 1' are then also slightly different.Generally the resulting difference in length is so slight (a few tenthsof a millimeter), that it need not be considered in the welding process,particularly when the coupling wires are welded on. Only with transducerresonators l and 1', it may happen that they become noticeably shortersince the piezoelectric member 8 preferably a ceramic transducer whichserves to excite and to transmit the mechanical vibrations,substantially reduces the inherent frequency when the length is the sameas that of the normal resonators. To compensate for this, the metalportions of the transducer resonator l', as well as the transducerresonator 1, must be shortened by up to about 2mm.

In order to prevent difficulties with the preferably substantiallystraight coupling wires 3, it is advantageous to employ a transducerresonator as shown in FIG. 8. Protrusions 9, as shown in FIG. 8, causethe total length of the transducer resonator l to become approximatelyequal to that of the resonators 2. The shape of these protrusions isalmost arbitrary. Of course, the transducer resonator l is provided withsimilar protrusions. In practice, the metallic portion of the transducerresonators l and l is provided, for exam ple, as an integral piece whichhas been machined to provide the protrusions 9, but these protrusionsmay also be welded on. The advantage is then that the weldedonprotrusions need not necessarily be made of a temperature compensatingmaterial.

The length of the transducer resonators l and 1' may, however, also beselected to equal that of the intervening resonators 2, if at the sametime the diameter of the transducer resonators l and l is increased.With the appropriate selection of length and diameter, tne inherentflexural resonant frequency remains substantially the same; however, thedistance of the transducer resonators l and 1' from the adjacentresonators 2 must be reduced due to the decrease in coupling.

The adaptation of the length may also be effected by a slight curvatureof coupling wires 13 fastened to the end surfaces of resonators l4 and15, as shown in FIG. 9, or by a variation of the lengths of a firsttransducer resonator 17, as well as of intervening resonators l8 and asecond transducer resonator (not shown), so that the filter has theapproximate construction shown in FIG. 10, coupling wires 16 beingessentially straight, but not parallel to one anodier.

FIG. ll shows another embodiment of an electromechanical filterconstructed in accordance with the present invention. All of theresonators 1, l, and 2 are connected in succession by means ofcouplingelements 3, e.g. thin wires preferably connected to theresonator end faces. Nonadjacent ones of the resonators are coupledtogether by additional coupling wires 3'.

The length of these wires corresponds approximately to the equation Itwill be understood that the above description of the present inventionis susceptible to various modifications, changes and adaptations and thesame are in tended to be comprehended within the meaning and range ofequivalents of the appended claims.

We claim:

1. An electromechanical filter having a signal input means and a signaloutput means comprising, in combination:

I. a first piezoelectrically acting transducer resonator having firstand second end surfaces and serving as said input means. a plurality ofintervening resonators of the fiexural vibrating type each having firstand second end surfaces, and a second piezoelectrically actingtransducer resonator having first and second end surfaces and serving assaid output means, said resonators being arranged substantially parallelto one another;

2. at least two thin longitudinally vibrating coupling wires. one ofsaid coupling wires being coupled to said first end surface of each saidresonator and another of said coupling wires being coupled to saidsecond end surface of each said resonator; and

3. a plurality of thin metal mounting strips fastened to saidresonators, the thickness and the length of each said mounting stripcorresponding approximately to the equation:

where d is the thickness of the metal strips, l is the length of themetal strips, (n is the angular frequency of the filter, p is thedensity of the metal strips, E is the modulus of elesticity of thematerial of the metal strips. and a is a constant having a valueselected from the group consisting of values of substantially 0.62; 0.1and 0.046.

2. An electromechanical filter as defined in claim 1, wherein theconstant a is substantially 0.62 and said fil ter exhibits \/4 typebehavior.

3. An electromechanical filter as defined in claim 1, wherein theconstant a is substantially 0.1 15, and said filter exhibits 3M4 typebehavior.

4. An electromechanical filter as defined in claim 1, wherein theconstant a is substantially 0.046, and said filter exhibits Sit/4 typebehavior.

5. An electromechanical filter as defined in claim 1, wherein said firstend surfaces and said second end surfaces are frontal faces of saidresonators.

6. An electromechanical filter as defined in claim 1, wherein the totalcross section of said coupling wires has a predetermined value.

7. An electromechanical filter as defined in claim 1, wherein each ofsaid resonators has a respective longitudinal axis, and wherein saidcoupling elements are arranged substantially parallel to one another andapproximately at a right angle to said longitudinal axis of saidresonators.

8. An electromechanical filter as defined in claim 1, further comprisingadditional coupling wires attached between nonadjacent resonatorsthereby to produce attenuation peaks at given real or complexfrequencies.

9. An electromechanical filter as defined in claim I, wherein each ofsaid metal strips is in the shape of a frame at least in that area whichis subjected to torsion stresses.

10. An electromechanical filter as defined in claim 9, wherein each saidframe has a respective opening having a height approximately equal tothe length of each of said metal strips and having a width of betweenabout one-third and one-half the length of each of said metal strips.

II. An electromechanical filter as defined in claim I, wherein all ofsaid resonators have the same resonant frequency and different lengthsand said coupling wires are curved so as to adapt them to the differinglengths of said resonators.

l2. An electromechanical filter as defined in claim I, wherein all ofsaid resonators have substantially the same resonant frequency and havesubstantially the same length and said two coupling wires are each substantially straight.

13. An electromechanical filter as defined in claim 12, wherein saidfirst and said second end surfaces of each said transducer resonator areeach provided with a respective axially extending protrusion having across section smaller than the cross section of each said transducerresonator, said two coupling wires being connected to said protrusions.

14. An electromechanical filter as defined in claim 12, wherein eachsaid resonator is substantially circular in radial cross section, thediameters of said transducer resonators being greater than the diametersof said intervening resonators.

15. An electromechanical filter as defined in claim 12, wherein eachsaid resonator is substantially circular in radial cross section, saidfirst transducer resonator. said intervening resonators and said secondtransducer resonator being arranged in succession, the lengths anddiameters of said resonators increasing progressively from one resonatorto the next.

16. An arrangement as defined in claim I, wherein said filterconstitutes a channel filter for a carrier frequency system.

17. A method of making an electromechanical filter comprising: providinga first transducer resonator. a

plurality of intervening resonators and a second transducer resonatoreach resonator having two end surfaces; fixing each resonator to amounting element; fine tuning the resonators by mechanically removingmaterial from at least one resonator after said step of fixing eachresonator to a mounting element; and, after said step of fine tuning,fixing coupling wires to the resonator end surfaces.

18. A method of making an electromechanical filter comprising: providinga first transducer resonator, a plurality of intervening resonators anda second transducer resonator each resonator having two end surfaces;forming mounting elements as thin metal strips of material forming theedge portions of a common piece of metal so as to form the mountingelements as parts of a single piece of metal; fixing the resonators tothe mounting elements; fixing coupling wires to the resonator endsurfaces; and fine tuning the resonators by mechanically removingmaterial from at least one resonator after said step of fixing eachresonator to a mounting element.

19. A method as defineil inclaim 18, wherein said step of forming themounting elements in the form of thin metal strips is effected bystamping out portions therebetween from the common piece of metal andsubsequently bending the meta] strips.

20. A method as defined in claim 18, wherein said step of forming themounting elements in the form of thin metal strips is effected byetching out portions therebetween from the common piece of metal andsubsequently bending the metal strips.

2]. A method as defined in claim 17, wherein the step of fixing theresonators is effected by spot welding, soldering, or cementing.

i i i k k

1. An electromechanical filter having a signal input means and a signaloutput means comprising, in combination:
 1. a first piezoelectricallyacting transducer resonator having first and second end surfaces andserving as said input means, a plurality of intervening resonators ofthe flexural vibrating type each having first and second end surfaces,and a second piezoelectrically acting transducer resonator having firstand second end surfaces and serving as said output means, saidresonators being arranged substantially parallel to one another;
 2. atleast two thin longitudinally vibrating coupling wires, one of saidcoupling wires being coupled to said first end surface of each saidresonator and another of said coupling wires being coupled to saidsecond end surface of each said resonator; and
 3. a plurality of thinmetal mounting strips fastened to said resonators, the thickness and thelength of each said mounting strip corresponding approximately to theequation: d/12 omega o Alpha square root Rho /E where d is the thicknessof the metal strips, 1 is the length of the metal strips, omega o is theangular frequency of the filter, Rho is the density of the metal strips,E is the modulus of elesticity of the material of the metal strips, andAlpha is a constant having a value selected from the group consisting ofvalues of substantially 0.62; 0.115; and 0.046.
 2. at least two thinlongitudinally vibrating coupling wires, one of said coupling wiresbeing coupled to said first end surface of each said resonator andanother of said coupling wires being coupled to said second end surfaceof each said resonator; and
 2. An electromechanical filter as defined inclaim 1, wherein the constant Alpha is substantially 0.62 and saidfilter exhibits lambda /4 - type behavior.
 3. An electromechanicalfilter as defined in claim 1, wherein the constant Alpha issubstantially 0.115, and said filter exhibits 3 lambda /4 - typebehavior.
 3. a plurality of thin metal mounting strips fastened to saidresonators, the thickness and the length of each said mounting stripcorresponding approximately to the equation: d/12 omega o Alpha SquareRoot Rho /E where d is the thickness of the metal strips, 1 is thelength of the metal strips, omega o is the angular frequency of thefilter, Rho is the density of the metal strips, E is the modulus ofelesticity of the material of the metal strips, and Alpha is a constanthaving a value selected from the group consisting of values ofsubstantially 0.62; 0.115; and 0.046.
 4. An electromechanical filter asdefined in claim 1, wherein the constant Alpha is substantially 0.046,and said filter exhibits 5 lambda /4 - type behavior.
 5. Anelectromechanical filter as defined in claim 1, wherein said first endsurfaces and said second end surfaces are frontal faces of saidresonators.
 6. An electromechanical filter as defined in claim 1,wherein the total cross section of said coupling wires has apredetermined value.
 7. An electromechanical filter as defined in claim1, wherein each of said resonators has a respective longitudinal axis,and wherein said coupling elements are arranged substantially parallelto one another and approximately at a right angle to said longitudinalaxis of said resonators.
 8. An electromechanical filter as defined inclaim 1, further comprising additional coupling wires attached betweennonadjacent resonators thereby to produce attenuation peaks at givenreal or complex frequencies.
 9. An electromechanical filter as definedin claim 1, wherein each of said metal strips is in the shape of a frameat least in that area which is subjected to torsion stresses.
 10. Anelectromechanical filter as defined in claim 9, wherein each said framehas a respective opening having a height approximately equal to thelength of each of said metal strips and having a width of between aboutone-third and one-half the length of each of said metal strips.
 11. Anelectromechanical filter as defined in claim 1, wherein all of saidresonators have the same resonant frequency and different lengths andsaid coupling wires are curved so as to adapt them to the differinglengths of said resonators.
 12. An electromechanical filter as definedin claim 1, wherein all of said resonators have substantially the sameresonant frequency and have substantially the same length and said twocoupling wires are each substantially straight.
 13. An electromechanicalfilter as defined in claim 12, wherein said first and said second endsurfaces of each said transducer resonator are each provided with arespective axially extending protrusion having a cross section smallerthan the cross section of each said transducer resonator, said twocoupling wires being connected to said protrusions.
 14. Anelectromechanical filter as defined in claim 12, wherein each saidresonator is substantially circular in radial cross section, thediameters of said transducer resonators being greater than the diametersof said intervening resonators.
 15. An electromechanical filter asdefined in claim 12, wherein each said resonator is substantiallycircular in radial cross section, said first transducer resonator, saidintervening resonators and said second transducer resonator beingarranged in succession, the lengths and diameters of said resonatorsincreasing progressively from one resonator to the next.
 16. Anarrangement as defined in claim 1, wherein said filter constitutes achannel filter for a carrier frequency system.
 17. A method of making anelectromechanical filter comprising: providing a first transducerresonator, a plurality of intervening resonators and a second transducerresonator each resonator having two end surfaces; fixing each resonatorto a mounting element; fine tuning the resonators by mechanicallyremoving material from at least one resonator after said step of fixingeach resonator to a mounting element; and, after said step of finetuning, fixing coupling wires to the resonator end surfaces.
 18. Amethod of making an electromechanical filter comprising: providing afirst transducer resonator, a plurality of intervening resonators and asecond transducer resonator each resonator having two end surfaces;forming mounting elements as thin metal strips of material forming theedge portions of a common piece of metal so as to form the mountingelements as parts of a single piece of metal; fixing the resonators tothe mounting elements; fixing coupling wires to the resonator endsurfaces; and fine tuning the resonators by mechanically removingmaterial from at least one resonator after said step of fixing eachresonator to a mounting element.
 19. A method as defined in claim 18,wherein said step of forming the mounting elements in the form of thinmetal strips is effected by stamping out portions therebetween from thecommon piece of metal and subsequently bending the metal strips.
 20. Amethod as defined in claim 18, wherein said step of forming the mountingelements in the form of thin metal strips is effected by etching outportions therebetween from the common piece of metal and subsequentlybending the metal strips.
 21. A method as defined in claim 17, whereinthe step of fixing the resonators is effected by spot welding,soldering, or cementing.